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Question

If - 3 + ix2y and x2+y+4i be conjugate of each other, then the value of x and y is
  1. None of these
  2. - 1 , 4


Solution

The correct option is A
We are given that ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯3+ ix2y= x2+y +4i (given)
i.e. - 3 - ix2y= x2+y+4i
3 = x2+y and x2y= 4
The quadratic equation whose roots are x2 and y is
t2 (x2+y) t+ x2 y 
t2+3t4=0
t = 4, t = 1
As x2   30, we taken x2 = 1 and y = 4
So, x = ± 1, y = 4

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